The 5D Mark III is not yet supported by the current or even the beta firmware for the Pocketwizard Flex units. You may be waiting a while before it is covered, like several months or more. Here is a link to their release plan:

It is not easy to make things work when you need to reverse engineer things, and Canon has no reason to keep things the same from camera to camera. In this case, there is a whole new type of Canon flash that Pocketwizard also needs to figure things out for, and the release plan says they will do that first before they do the 5D3.

Hmm....I just did some testing with my new 5DM3 and the TT5 & TT1, and they all worked perfectly together. Now, I do not have the latest software update, I don't think I've updated in a year or so. So I'm wondering if that is why it works?